Hardness of Online Sleeping Combinatorial Optimization Problems

Abstract

We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the sleeping versions of these problems are at least as hard as PAC learning DNF expressions, a long standing open problem. We show hardness for the sleeping versions of Online Shortest Paths, Online Minimum Spanning Tree, Online k-Subsets, Online k-Truncated Permutations, Online Minimum Cut, and Online Bipartite Matching. The hardness result for the sleeping version of the Online Shortest Paths problem resolves an open problem presented at COLT 2015 [Koolen et al., 2015].

Cite

Text

Kale et al. "Hardness of Online Sleeping Combinatorial Optimization Problems." Neural Information Processing Systems, 2016.

Markdown

[Kale et al. "Hardness of Online Sleeping Combinatorial Optimization Problems." Neural Information Processing Systems, 2016.](https://mlanthology.org/neurips/2016/kale2016neurips-hardness/)

BibTeX

@inproceedings{kale2016neurips-hardness,
  title     = {{Hardness of Online Sleeping Combinatorial Optimization Problems}},
  author    = {Kale, Satyen and Lee, Chansoo and Pal, David},
  booktitle = {Neural Information Processing Systems},
  year      = {2016},
  pages     = {2181-2189},
  url       = {https://mlanthology.org/neurips/2016/kale2016neurips-hardness/}
}